An algebraic expression combines constants, variables and operations. A variable can stand for a measurement that changes, such as the width of a rectangle. Substituting particular values evaluates the expression, whereas simplifying produces an equivalent expression for every allowed input.
Substitute negative numbers with parentheses
Evaluate the expression below at x equal to −2. Parentheses keep the negative sign inside the base of the square. The squared term contributes 12, the linear term contributes 4 and the constant adds 1.
Identify terms, coefficients and degree
A monomial is a constant times variables raised to nonnegative integer powers. The degree of a nonzero monomial is the sum of those exponents. A polynomial is a finite sum of monomials, so a single monomial also counts as a polynomial. After combining like terms, the degree of a nonzero polynomial is the largest term degree. Expressions with a variable in a denominator or under a square root can be algebraic without being polynomials.
Combine like terms and distribute products
Terms are like terms when their variable parts have exactly the same powers. Add or subtract their coefficients and leave the variable part intact. When multiplying monomials, multiply the coefficients and add exponents of each shared base. For a product with a sum, multiply every term inside the parentheses. When subtracting a polynomial, distribute the minus sign to every term being subtracted.
Keep excluded values when canceling factors
You can divide out a common factor in a quotient where that factor is nonzero. You cannot cancel an isolated term across addition or subtraction. Factor the numerator in the example below before canceling. The simplified expression agrees with the original only for x different from zero.
